The little Mermaid

I read a book of the little Mermaid. Little mermaid is princess of the sea. She is in love with a prince who is people. But she can't meet him because she is mermaid and he is people. One day, she ask a witch to make her be a people. She can be people by the grace of witch. She meet a prince at last. But they were not in love with each other. She goes back to the sea.
The story of little mermaid I know is different from this story. I don't like this enging.